**Bias Circuit Thermal Stability:**

**V _{BE} and I_{CBO} Variations** – Many transistor circuits are required to operate over a wide temperature range. So, another aspect of bias circuit stability is Bias Circuit Thermal Stability, or how stable I

_{C}and V

_{CE}remain when the circuit temperature changes.

Measures to deal with the effects of h_{FE} variations have already been discussed. These apply whether the different h_{FE} values are due to temperature changes or to h_{FE} differences from one transistor to another.

The base-emitter voltage (V_{BE}) and the collector-base reverse, saturation current (I_{CBO}) are the two temperature-sensitive quantities that largely determine the Bias Circuit Thermal Stability of a transistor circuit, [see Fig. 5-48(a)]. The base-emitter and collector-base pn-junctions have the temperature characteristics. For a silicon transistor, V_{BE} changes by approximately -1.8 mV/°C, and I_{CBO} approximately doubles for every 10°C rise in temperature. These effects are illustrated by the characteristics in Fig. 5-48(b) and (c).

An increase in I_{CBO} causes I_{C} to be larger, and the I_{C} increase raises the collector-base junction temperature. This, in turn, results in a further increase in I_{CBO}. The effect is cumulative, so that the end result might be a substantial collector current increase. This could produce a significant shift in the circuit Q-point, or in the worst case, I_{C} might keep on increasing until the transistor collector-base junction overheats and burns out. This effect is known as thermal runaway. Measures taken to avoid thermal runaway are similar to those required for good bias stability against h_{FE} spread.

Changes in V_{BE} may also produce significant changes in I_{C} and consequently in the circuit Q-point. However, because of the possibility of thermal runaway, I_{CBO} changes are the most important. The Bias Circuit Thermal Stability is assessed by calculating a stability factor.

**Stability Factor:**

The stability factor (S) of a circuit is the ratio of the change in collector current to the change in collector-base leakage current.

The value of S depends on the circuit configuration and on the resistor values. The minimum values of S is 1. This means that if I_{CBO} increases by 1 μA I_{C} will increase by 1 μA. If a circuit has an S of 50, then ΔI_{C} = 50 x ΔI_{CBO}. A stability factor of 50 (or larger) is considered poor, while a factor of 10 or less is considered good.

An equation for the stability factor of a bias circuit can be derived by writing an equation for the circuit I_{C} and investigating the effect of I_{CBO }change. The stability factors for the three basic bias circuit types (reproduced in Fig. 5-49) can be shown to be:

For base bias,

For collector-to-base bias,

For voltage divider bias,

The change in I_{CBO} over a given temperature range can be calculated by recalling that I_{CBO} doubles for every 10°C increase in temperature. The temperature change (ΔT) is divided by 10 to give the number of 10°C changes (n). If the starting level of collector-base leakage current is I_{CBO(1)}, the new level is,

The I_{CBO} change and the circuit stability factor can be used to determine the change in I_{C}, (Eq. 5-18). Then the resulting V_{CE} change can be investigated.

**Effect of V**_{BE }Changes:

_{BE }Changes:

Consider the voltage divider bias circuits in Fig. 5-51(a) and (b), which each have V_{CC} = 12 V and I_{C} = 1 mA. From Eq. 5-9,

Assuming that V_{B} remains substantially constant, an equation for I_{C} change with V_{BE} change can be written:

As discussed already, the emitter resistor voltage should typically be selected as 5 V, (V_{E} >> V_{BE}). This is to ensure that I_{C} is not significantly affected by changes in V_{BE}. Thus, the circuit in Fig. 5-51(a) (with V_{E} ≈ 5 V) has greater stability against V_{BE} changes than the one in Fig. 5-51(b) which was designed for V_{E} = V_{CC}/10,(V_{E }= 1.2V).

**Diode Compensation:**

The use of a diode to compensate for V_{BE} changes is illustrated in Fig. 5-52. In this case,

When V_{BE} changes by ΔV_{BE}, the diode voltage changes by an approximately equal amount (ΔV_{D1}). ΔV_{BE} and ΔV_{D1} tend to cancel each other, leaving I_{C }largely constant at,

Base bias and collector-to-base bias are less affected by V_{BE} changes than voltage divider bias. This can easily be demonstrated by considering the equations for the base current in each case.